api mpms 14.3.3

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~ ~ API MPMS*L4-3.3 92 W 0732290 053b085 556 Date of Issue: March 1994 Affected Publication: API Chapter 14 “Natural Gas Fluids Measurement,” Section 3, “Concentric, Square-Edged Orifice Meters,” Part 3, “Natural Gas Applications” of the Manual of Petroleum Measurement Standards, Third Edition, August 1992 ERRATA On page 25, Equation 3-A-IO should read as follows: g, = 0.0328096[978.01855 - 0.0028247L + 0.0020299L2 - 0.000015085L3 - 0.000094Hl (3-A-10) On page 33, Equation 3-B-9 should read as follows: O7 cl = 0.000511 + [O.O2iû + 0.0049( 19, OOOß 7*]p4(- 1,000,000 I J35 (3-B-9) ReD Re, On page 56, the second equation under 34.3. I. 7 should read as follows: Q,( 14.73)(0.570) ( (0.00OO069)(S.0î085)(5 19.67)(0.999590) ReD = (0.0114541) = 3.324464 On page 57, Equation 3-6b should read as follows: = 7709.6 1 (0.60)( 1 .O3 1 60)(0.998383)( 3.99%9)2 (O. 5 70) (O. 9 5 1 308) (5 24.67) = 614,033 cubic feet per hour at standard conditions On page 57, the second equation in 3-6b should read as follows: Re, = 3.32446Q,. = 3.32446(614,033) = 2,041,328 (initial estimate of Reynolds number) (3-6b)

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  • ~ ~

    A P I MPMS*L4-3.3 92 W 0732290 053b085 556

    Date of Issue: March 1994 Affected Publication: API Chapter 14 Natural Gas Fluids Measurement, Section 3, Concentric, Square-Edged Orifice Meters, Part 3, Natural Gas Applications of the Manual of Petroleum Measurement Standards, Third Edition, August 1992

    ERRATA

    On page 25, Equation 3-A-IO should read as follows:

    g, = 0.0328096[978.01855 - 0.0028247L + 0.0020299L2 - 0.000015085L3 - 0.000094Hl (3-A-10)

    On page 33, Equation 3-B-9 should read as follows: O 7

    cl = 0.000511 + [O.O2i + 0.0049( 19, OOO 7* ]p4 ( - 1,000,000 I J35 (3-B-9)

    ReD Re,

    On page 56, the second equation under 34.3. I . 7 should read as follows:

    Q,( 14.73)(0.570) ( (0.00OO069)(S.0085)(5 19.67)(0.999590) ReD = (0.0114541) = 3.324464

    On page 57, Equation 3-6b should read as follows:

    = 7709.6 1 (0.60)( 1 .O3 1 60)( 0.9983 83)( 3 .99%9)2

    (O. 5 70) (O. 9 5 1 308) (5 24.67) = 614,033 cubic feet per hour at standard conditions

    On page 57, the second equation in 3-6b should read as follows:

    Re, = 3.32446Q,. = 3.32446(614,033) = 2,041,328 (initial estimate of Reynolds number)

    (3-6b)

  • ~ ~~

    API MPMS+lY.3-3 92 0732290 0536086 492

    On page 57, Equation 3-20 should read as follows:

    19, OOO A = ( r ) 0 8

    - - [ 19, 000(0.495597)]0 * 2,041,328

    = 0.0135262

    On page 57, Equation 3-21 should read as follows:

    2,041,328 = 0.778988

    (3-20)

    (3-21)

    On page 58, Equation 3-15 should read as follows:

    Upstrm = C0.0433 + 0.0712e-85L1 - 0.1145e-60L'](1 - 0.23A)B

    (3-15) = C0.0433 + 0.0712es~"'*' - 0.1145e6~u708s] x [i - 0.23(0.0135262)](0.0642005)

    = 0.000876388

    On page 58, Equation 3-16 should read as follows:

    Dnstrm = -0.0116[M2 - 0.52M~3]'1(l - 0.14A)

    = - 0.01 16[0.491284 - 0.52(0.491284)'3](0.495597)' ' (3-16)

    x [i - 0.14(0.0135262)] = - 0.00152379

    On page 58, Equation 3-14 should read as follows: Tap Term = Upstrm + Dnstrm

    = 0.000876388 + (-0.00152379) (3-14) = - 0.000647402

    On page 58, Equation 3-12 should read as follows:

    C,(F) = C,.(CT) + Tap Tem = 0.602414 - 0.000647402 = 0.601767

    (3-12)

    On page 58, Equation 3-11 should read as follows:

    C,(FT) = C,(FT) + 0.000511 + (0.0210 + 0.0049A)P4C

    = 0.601767 + 0.000511 [ 1O6(O.495597)]u7 2,041,328

    (3-11)

    + [0.0210 + 0.0049(0.0135262)](0.495597)4(0.778988) = 0.602947 (second estimate of the coefficient of discharge)

    2

  • On page 58, the third to the last equation should read as follows: Qv = 617,048 cubic feet per hour at standard conditions

    [based on C, (F) = 0.6029471

    On page 58, the second to the last equation should read as follows: Re, = 3.32446Q,, = 3.32446(617,048)

    = 2,05 1,35 1 (second estimate of Reynolds number)

    On page 59, the second equation should read as follows: Re, = 3.32446Qv = 3.32446(617,046)

    = 2,05 1,345 (third estimate of Reynolds number)

    On page 59, Equation 3-7 should read as follows:

    = 6 17,046(-)( 14.73 -)( 509.67 0.997839\, 14.65 519.67 0.997971)

    (3- 7)

    = 608,396 cubic feet per hour at base conditions

    On page 60, Equation 3-B-9 should read as follows:

    1,000, ooop ( 'i e, = 0.000511 o 3 5 (3-8-9)

    1,000,000

    On page 62, the$rst equation should read as follows:

    = 0.5961 + 0.0291p2 - 0.2290px

    + (0.0433 + 0.0712en% - 0.1 1456') [ 1 - 0.23 ( -'- i9:;p)..] - p;'

    = 0.5961 + 0.0291(0.495597)2 - 0.2290(0.495597)* + [ 0.0433 + 0.0712e"07"~ - 0.1 145e6'07"')[l - 0.23(0.0137493)](0.0642005) - 0.01 16[0.491284 - 0.52(0.49128413)](0.495597)'.1[1 - 0.14(0.0137493)]

    = 0.601767

    3

  • A P I M P M S * 1 4 - 3 . 3 92 0732290 0536088 265

    On page 62, Equation 3-B-9 should read as follows:

    4 = 0.000511 (1 ,00 ;~00~)" '

    0.0210 + 0.0049 ( 1 9 , 0 0 0 ~ ~ )"*]].(i, ooo,ooo 1 35 Re, Re,

    = 0.000511( 1,000,000(0.495597) 2,000,000

    (3-8-9)

    + [0.02 1 O + 0.0049(0.0 137493)](0.495597)'(0.784584) = 0.00118960

    On page 65, thefirst equation should read as follows:

    Re, = 0.0114588 - (",or) = 3.32446Q" = 3.32446(617,057) = 2,05 1,400 (second iteration)

    On page SO, Equation 3-0-9 should read as follows (that is, Kpipe, should be inserted in the equation and the second line of the equation should be deleted}:

    Re, = 2 2 0 , 8 5 8 d l $ m x (Kpipe) (3-0-9)

    On page 80, the nomenclature should read as follows (that is, Kpipe, should be inserted in the list):

    Where:

    G = specific gravity. Kpipe = values from Table 3-D-4.

    Red = orifice bore Reynolds number. T, = absolute flowing temperature, in degrees Rankine. p = specific weight of a gas at 14.7 pounds force per squareinch absolute and 32F

    On page 97, Equations 3-F-4 and 3-F-5 should read as follows:

    Hid = 4,(ff:d), + 4 2 W i d ) 2 + ... + 4wwid)w (3-F-4)

    On page 102, the second line of Equation 3-4a should read as follows:

    (3-F-5)

    ZbRT G, (28.9625)(144)hw eG,(28.9625)(144)

    Qb = 359.072C,(FT)Evqd2

    4

  • A P I M P M S * L 4 . 3 * 3 92 0732290 0503843 988

    Manual of Petroleum Measurement Standards Chapter 14-Natural Gas Fluids

    Measurement Section 3-Concentric, Square-Edged

    Orif ice Meters Part 3-Natural Gas Applications THIRD EDITION, AUGUST 1992

    I ACA American Gas Association Report No. 3, Part 3 I I i;pp Gas Processors Association GPA 81 85, Part 3 1 American National Standards Institute ANSVAPI 2530-1 991, Part 3 I

    American Petroleum Institute 1220 L Street. Northwest

    11 Washington, D.C. 20005

  • A P I M P M S * 1 4 - 3 a 3 92 0732290 0503844 814

    Manual of Petroleum Measurement Standards Chapter 14-Natural Gas Fluids Measurement Section 3-Concentric, Square-Edged

    Orif ice Meters Part 3-Natural Gas Applications

    Measurement Coordination Department

    THIRD EDITION, AUGUST 1992

    American Petroleum Institute

  • ~ ~ ~~~

    API M P M S * L 4 - 3 . 3 92 m 0732290 0503845 750 m

    SPECIAL NOTES

    1. API PUBLICATIONS NECESSARILY ADDRESS PROBLEMS OF A GENERAL NATURE. WITH RESPECT TO PARTICULAR CIRCUMSTANCES, LOCAL, STATE, AND FEDERAL LAWS AND REGULATIONS SHOULD BE REVEWED.

    2. API IS NOT UNDERTAKING TO MEET THE DUTIES OF EMPLOYERS, MANU- FACTURERS, OR SUPPLIERS TO WARN AND PROPERLY TRAIN AND EQUIP THEIR EMPLOYEES, AND OTHERS EXPOSED, CONCERNING HEALTH AND SAFETY RISKS AND PRECAUTIONS, NOR UNDERTAKING THEIR OBLIGATIONS UNDER LOCAL, STATE, OR FEDERAL LAWS.

    3. INFORMATION CONCERNING SAFETY AND HEALTH RISKS AND PROPER

    TIONS SHOULD BE OBTAINED FROM THE EMPLOYER, THE MANUFACTURER OR SUPPLIER OF THAT MATERIAL, OR THE MATERIAL SAFETY DATA SHEET.

    4. NOTHING CONTAINED IN ANY API PUBLICATION IS TO BE CONSTRUED AS

    PRECAUTIONS WITH RESPECT TO PARTICULAR MATERIALS AND CONDI-

    GRANTING ANY RIGHT, BY IMPLICATION OR OTHERWISE, FOR THE MANU- FACTURE, SALE, OR USE OF ANY METHOD, APPARATUS, OR PRODUCT COV- ERED BY LETTERS PATENT. NEITHER SHOULD ANYTHING CONTAINED IN

    ITY FOR INFRINGEMENT OF LETI'ERS PATENT. THE PUBLICATION BE CONSTRUED AS INSURING ANYONE AGAINST LIABIL-

    5. GENERALLY, API STANDARDS ARE REVIEWED AND REVISED, REAF- FIRMED, OR WITHDRAWN AT LEAST EVERY FIVE YEARS. SOMETIMES A ONE- TIME EXTENSION OF UP TO TWO YEARS WILL BE ADDED TO THIS REVIEW

    TER ITS PUBLICATION DATE AS AN OPERATIVE API STANDARD OR, WHERE AN EXTENSION HAS BEEN GRANTED, UPON REPUBLICATION. STATUS OF THE

    CYCLE. THIS PUBLICATION WILL NO LONGER BE IN EFFECT FIVE YEARS AF-

    PUBLICATION CAN BE ASCERTAINED FROM THE API AUTHORING DEPART- MENT [TELEPHONE (202) 682-8000]. A CATALOG OF API PUBLICATIONS AND MATERIALS IS PUBLISHED ANNUALLY AND UPDATED QUARTERLY BY API, 1220 L STREET, N. W., WASHINGTON, D.C. 20005.

    Copyright O 1992 American Petroleum Institute

  • FOREWORD

    This foreword is for information and is not part of this standard. Chapter 14, Section 3, Part 3, of the Manual of Petroleum Measurement Standards pro-

    vides an application guide along with practical guidelines for applying Chapter 14, Section 3, Parts 1 and 2, to the measurement of natural gas. Mass flow rate and base (or standard) volumetric flow rate methods are presented in conformance with North American industry practices.

    This standard has been developed through the cooperative efforts of many individuals from industry under the sponsorship of the American Petroleum Institute, the American Gas Association, and the Gas Processors Association, with contributions from the Chemical Manufacturers Association, the Canadian Gas Association, the European Community, Nor- way, Japan, and others.

    API publications may be used by anyone desiring to do so. Every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them; however, the Institute makes no representation, warranty, or guarantee in connection with this pub- lication and hereby expressly disclaims any liability or responsibility for loss or damage re- sulting from its use or for the violation of any federal, state, or municipal regulation with which this publication may conflict.

    Suggested revisions are invited and should be submitted to the director of the Measure- ment Coordination Department, American Petroleum Institute, 1220 L Street, N.W., Wash- ington, D.C. 2000.5.

    i i i

  • ACKNOWLEDGMENTS

    From the initial data-collection phase through the final publication of this revision of Chapter 14, Section 3, of the Manual of Petroleum Measurement Standards, many individ- uals have devoted time and technical expertise. However, a small group of individuals has been very active for much of the project life. This group includes the following people:

    H. Bean, El Paso Natural Gas Company (Retired) R. Beaty, Amoco Production Company, Committee Chairman D. Bell, NOVA Corporation T. Coker, Phillips Petroleum Company W. Fling, OXY USA, Inc. (Retired), Project Manager J. Gallagher, Shell Pipe Line Corporation L. Hillburn, Phillips Petroleum Company (Retired) P. Hoglund, Washington Natural Gas Company (Retired) P. LaNasa G. Less, Natural Gas Pipeline Company of America (Retired) J. Messmer, Chevron U.S.A. Inc. (Retired) R. Teyssandier, Texaco Inc.

    K. West, Mobil Research and Development Corporation E- UPP

    During much of the corresponding time period, a similar effort occurred in Europe. The following individuals provided valuable liaison between the two efforts:

    D. Gould, Commission of the European Communities F, Kinghorn, National Engineering Laboratory M. Reader-Harris, National Engineering Laboratory J. Sattary, National Engineering Laboratory E. Spencer, Consultant J. Stolz, Consultant P. van der Kam, Gasunie

    The American Petroleum Institute provided most of the funding for the research project. Additional support was provided by the Gas Processors Association and the American Gas Association. Special thanks is given to the Gas Research Institute and K. Kothari for pro- viding funding and manpower for the natural gas calculations used in this project and to the National Institute of Standards and Technology in Boulder, Colorado, for additional flow work.

    J. Whetstone and J. Brennan were responsible for the collection of water data at the Na- tional Institute of Standards and Technology in Gaithersburg, Maryland. C. Britton, S. Cald- well, and W. Seid1 of the Colorado Engineering Experiment Station Inc. were responsible for the oil data. G. Less, J. Brennan, J. Ely, C. Sindt, K. Starling, and R. Ellington were re- sponsible for the Natural Gas Pipeline Company of America test data on natural gas.

    Over the years many individuals have been a part of the Chapter 14.3 Working Group and its many task forces. The list below is the roster of the working group and its task forces at the time of publication but is by no means a complete list of the individuals who partic- ipated in the development of this document.

    R. Adamski, Exxon Chemical Americas-BOP R. Bass M. Bayliss, Occidental Petroleum (Caledonia) Ltd. R. Beaty, Amoco Production Company D. Bell, NOVA Corporation B. Berry J. Bosio, Statoil

    iv

  • -

    API MPMS*L4-3-3 92 = 0732290 0503848 4bT =

    J. Brennan, National Institute of Standards and Technology E. Buxton S. Caldwell T. Coker, Phillips Petroleum Company H. Colvard, Exxon Company, U.S.A. L. Datta-Bania, United Gas Pipeline Company D. Embry, Phillips Petroleum Company

    J. Gallagher, Shell Pipe Line Corporation V. Gebben, Kerr-McGee Corporation B. George, Amoco Production Company G. Givens, CNG Transmission Corporation T. Glazebrook, Tenneco Gas Transportation Company D. Goedde, Texas Gas Transmission Corporation D. Gould, Commission of the European Communities K. Gray, Phillips Petroleum Company R. Hankinson, Phillips 66 Natural Gas Company R. Haworth E. Hickl, Union Carbide Corporation L. Hillburn P. Hoglund, Washington Natural Gas Company J. Hord, National Institute of Standards and Technology E. Jones, Jr., Chevron Oil Field Research Company M. Keady K. Kothari, Gas Research Institute P. LaNasa G. Less G. Lynn, Oklahoma Natural Gas Company R. Maddox G. Mattingly, National Institute of Standards and Technology B. McConaghy, NOVA Corporation C. Mentz L. Norris, Exxon Production Research Company K. Olson, Chemical Manufacturers Association A. Raether, Gas Company of New Mexico E. Raper, OXY USA, Inc. W. Ryan, El Paso Natural Gas Company R. Segers J. Sheffield S. Stark, Williams Natural Gas Company K. Starling J. Stolz J. Stuart, Pacific Gas and Electric Company W. Studzinski, NOVA/Husky Research Company M. Sutton, Gas Processors Association R. Teyssandier, Texaco Inc. V. Ting, Chevron Oil Field Research Company L. Traweek, American Gas Association

    E Van Orsdol, Chevron U.S.A. Inc. N. Watanabe, National Research Laboratory of Metrology, Japan K. West, Mobil Research and Development Corporation P. Wilcox, Total of France J. Williams, Oryx Energy Company

    w. Fling

    E. UPP

    V

  • M. Williams, Amoco Production Company E. Woomer, United Gas Pipeline Company C. Worrell, OXY USA, Inc.

    vi

  • ~~ ~ . ._ -

    A P I MPMS*1V-3.3 92 = 0732290 0503850 018 W

    CONTENTS

    Page

    CHAPTER 14 -NATURAL GAS FLUIDS MEASUREMENT SECTION 3 .CONCENTRIC. SQUARE-EDGED

    ORIFICE METERS 3.1 Introduction ..................................................................................................... 1

    3.1.1 Application ............................................................................................... 1 3.1.2 Basis for Equations ................................................................................... 1 3.1.3 Organization of Part 3 .............................................................................. 1

    3.2 Symbols. Units. and Terminology ................................................................... 1 3.2.1 General ..................................................................................................... 1 3.2.2 Symbols and Units ................................................................................... 2 3.2.3 Terminology ............................................................................................. 4

    3.3 Flow Measurement Equations ......................................................................... 5 3.3.1 General ..................................................................................................... 3.3.2 Equations for Mass Flow of Natural Gas ................................................. 3.3.3 Equations for Volume Flow of Natural Gas ............................................. 3.3.4 Volume Conversion From Standard to Base Conditions ..........................

    Flow Equation Components Requiring Additional Computation ................... 3.4.1 General ..................................................................................................... 3.4.2 Diameter Ratio ......................................................................................... 3.4.3 Coefficient of Discharge for Flange-Tapped Orifice Meter ..................... 3.4.4 Velocity of Approach Factor .................................................................... 3.4.5 Reynolds Number ..................................................................................... 3.4.6 Expansion Factor ......................................................................................

    3.4

    3.5 Gas Properties ................................................................................................. 3.5.1 General ..................................................................................................... 3.5.2 Physical Properties ................................................................................... 3.5.3 Compressibility ........................................................................................ 3.5.4 Relative Density (Specific Gravity) .........................................................

    Density of Fluid at Flowing Conditions ................................................... 3.5.5

    5 5 6 7 7 7 8 8

    10 10 11 13 13 13 14 15 17

    APPENDIX 3-A-ADJUSTMENTS FOR INSTRUMENT CALIBRATION ....... 21 APPENDIX 3-B-FACTORS APPROACH .......................................................... 29 APPENDIX 3-C-FLOW CALCULATION EXAMPLES .................................... 53 APPENDIX 3-D-PIPE TAP ORIFICE METERING ........................................... 67 APPENDIX 3-E-SI CONVERSIONS .................................................................. 91 APPENDIX 3-F-HEATING VALUE CALCULATION ...................................... 95 APPENDIX 3-G-DEVELOPMENT OF CONSTANTS FOR

    FLOW EQUATIONS ............................................................... 99

    Figures 3-D-1-Maximum Percentage Allowable Meter Tube Tolerance Versus

    Beta Ratio ................................................................................................. 73 78 3-D-2-Allowable Variations in Pressure Tap Hole Location ..............................

    Tables 3-1-Linear Coefficient of Thermal Expansion .................................................. 8

    24 3-A-2-Mercury Manometer Factors (Fhgm) ....................................................... 27 3-B-1-Assumed Reynolds Numbers for Various Meter Tube Sizes ................. 35 3-B-2-Numeric Conversion Factor (E) ............................................................ 36 3-B-3-Orifice Calculation Factor: F, From Equations in 3-B.5 ........................ 39

    3-A- 1-Water Density Based on Wegenbreth Equation ......................................

  • - - ._ -_ A P I NPflS*l14-3 .3 92 m 0732290 0503851 T 5 4 m

    3-B-4-Orifice Slope Factor: F,, From Equations in 3-B.6 .................................. 3-B-5-Conversion of ReD/106 to Q,/lOOO (Qv in Thousands of

    Cubic Feet per Hour) ............................................................................. 3-B-6-Expansion Factors for Flange Taps (Y,): Static Pressure Taken From

    Upstream Taps ........ .......... ..... ..... .. ..... .. .. ..... ..... .. ....... .. .. ..... .. .. .. ..... .. .... .. . 3-B-7-F,b Factors Used to Change From a Pressure Base of 14.73 Pounds

    Force per Square Inch to Other Pressure Bases ..................................... 3-B-8-&, Factors Used to Change From a Temperature Base of 60F to Other

    Temperature Bases ........... .. ..... .. ..... ....... .. ..... ... .. ....... .. .... ..... .. .. ....... .. ...... 3-B-9-I$Factors Used to Change From a Flowing Temperature of 60F to

    Actual Flowing Temperature .................................................................. 3-B-lO-F,,. Factors Used to Adjust for Real Gas Relative Density (GJ: Base

    Conditions of 60F and 14.73 Pounds Force per Square Inch Absolute 3-B-11-Supercompressibility Factors for G,. = 0.6 Without Nitrogen or

    Carbon Dioxide ........... .............. ................... .. .....,.......... ......... .. ..... ...... 3-D-1-Basic Orifice Factors (Fb) for Pipe Taps ................................................. 3-D-2-Meter Tube Pressure Tap Holes ............ .. ..... ......... ......... ....... .. ......... .. .. .. 3-D-3-b Values for Determining Reynolds Number Factor F, for Pipe Taps ... 3-D-4-Values of K to Be Used in Determining Rd for Calculation of F, Factor.. 3-D-5-Expansion Factors for Pipe Taps (YJ: Static Pressure Taken From

    Upstream Taps ... .. . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-D-6-Expansion Factors for Pipe Taps (Y2): Static Pressure Taken From

    Downstream Taps ................................................................................... 3-E- 1-Volume Reference Conditions for Custody Transfer Operations:

    Natural Gas Volume ............................................................................... 3-E-2-Energy Reference Conditions ..... . . , , . . . , , . , , . . . . . . . . . . . , . . , . . . . , . . , . . . . , . . . . . . . . , . . . . . . . . . . . 3-E-3 -Heating Value Reference Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-F-1-Physical Properties of Gases at Exactly 14.73 Pounds Force per Square

    Inch Absolute and 60F ..........................................................................

    Page

    42

    44

    47

    49

    49

    50

    51

    52 74 78 80 84

    85

    87

    93 93 93

    96

    viii

  • Chapter 14-Natural Gas Fluids Measurement

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS

    PART 3-NATURAL GAS APPLICATION

    3.1 Introduction 3.1 .I APPLICATION 3.1 .I .I General

    This part of Chapter 14, Section 3, has been developed as an application guide for the calculation of natural gas flow through a flange-tapped, concentric orifice meter, using the inch-pound system of units. For applications involving SI units, a conversion factor may be applied to the results (Q,, Qv, or Qb) determined from the equations in 3.3. Intermediate conversion of units will not necesskly produce consistent results. As an alternative, the more universal approach specified in Chapter 14, Section 3, Part 1, should be used. The me- ter must be constructed and installed in accordance with Chapter 14, Section 3, Part 2.

    3.1 .I .2 Definition of Natural Gas As used in this part, the term natural gas applies to fluids that for all practical purposes

    are considered to include both pipeline- and production-quality gas with single-phase flow and mole percentage ranges of components as given in American Gas Association (A.G.A.) Transmission Measurement Committee Report No. 8, Compressibility and Supercom- pressibility for Natural Gas and Other Hydrocarbon Gases. For other hydrocarbon mix- tures, the more universal approach specified in Part 1 may be more applicable. Diluents or mixtures other than those stipulated in A.G.A. Transmission Measurement Committee Re- port No.8 may increase the flow measurement uncertainty.

    3.1.2 BASIS FOR EQUATIONS The computation methods used in this part are consistent with those developed in Part 1

    and include the Reader-Harris/Gallagher equation for flange-tapped orifice meter discharge coefficient. The equation has been modified to reflect the more common units of the inch- pound system. Since the new coefficient of discharge equation does not address pipe tap meters, the pipe tap methodology of the 1985 edition of ANSUAPI 2530 has been retained for reference in Appendix 3-D.

    3.1.3 ORGANIZATION OF PART 3 Chapter 14, Section 3, Part 3, is organized as follows: Symbols and units are defined in

    3.2, the basic flow equation is presented in 3.3, the key equation components are defined in 3.4, and the gas properties applicable to orifice metering of natural gas are developed in 3.5. All values are assumed to be absolute. Factors to compensate for meter calibration and lo- cation are included in Appendix 3-A. The factor approach to orifice measurement is in- cluded in Appendix 3-B. Appendix 3-C covers examples to assist the user in interpreting this part. Appendix 3-D covers pipe tap meters. Appendix 3-E covers SI conversions, Ap- pendix 3-F covers heating value calculation, and Appendix 3-G covers derivation of con- stants. The user is cautioned that the symbols as defined in 3.2 may be different from those used in previous orifice metering standards.

    3.2 Symbols, Units, and Terminology 3.2.1 GENERAL

    The symbols and units used are specific to Chapter 14, Section 3, Part 3, and were devel- oped based on the customary inch-pound system of units. Regular conversion factors can

    1

  • ~~

    A P I MPMS*L4.3-3 92 E 0732290 0503853 827

    2 CHAPTER 1 '&NATURAL GAS FLUIDS MEASUREMENT

    be used where applicable; however, if SI units are used, the more generic equations in Part 1 should be used for consistent results.

    3.2.2 SYMBOLS AND UNITS Description

    Orifice plate coefficient of discharge Coefficient of discharge at a specified pipe Reynolds number for Bange-tapped orifice meter Coefficient of discharge at infinite pipe Reynolds number for coiner-tapped orifice meter Coefficient of discharge at infinite pipe Reynolds number for Bange-tapped orifice meter Specific heat at constant pressure Specific heat at constant volume Orifice plate bore diameter calculated at flowing temperature, T, Meter tube internal diameter calculated at flowing temperature, $ Orifice plate bore diameter calculated at reference temperature, T, Meter tube internal diameter calculated at reference temperature, T, Napierian constant Velocity of approach factor Temperature, in degrees Fahrenheit Temperature, in degrees Rankine Supercompressibility factor Gas relative density (specific gravity) Ideal gas relative density (specific gravity) Real gas relative density (specific gravity) Orifice differential pressure Isentropic exponent (see 3.4.5) Ideal gas isentropic exponent Perfect gas isentropic exponent Real gas isentropic exponent Mass Molar mass (molecular weight) of air Molar mass (molecular weight) of gas Molar mass (molecular weight) of componen1 Number of moles Unit conversion factor (discharge coefficient) Pressure Base pressure Base pressure of air Base pressure of gas Static pressure of fluid at the pressure tap Absolute static pressure at the orifice upstream differential pressure tap Absolute static pressure at the orifice downstream differential pressure tap

    Units/Value -

    -

    Btu/(lbm-OF) B tu/(lbm-OF)

    in

    in

    in

    in 2.7 1828

    -

    459.67 + O F

    inches of water column at 60F

    -

    lbm 28.9625 lbm/ib-mol lbmfib-mol lbmbb-mol

    -

    lbf/in2 (abs) lbf/in2 (abs) ibf/in* (abs) lbf/in2 (abs) lbf/in2 (abs)

    lbf/in2 (abs)

    lbf/in2 (abs)

  • SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART Q-NATURAL GAS APPLICATIONS 3

    Standard pressure Volume flow rate at base conditions Mass flow rate per second Mass flow rate per hour Volume flow rate per hour at standard conditions Universal gas constant Pipe Reynolds number Temperature Base temperature Base temperature of air Base temperature of gas Temperature of fluid at flowing conditions Reference temperature of the orifice plate bore diameter and/or meter tube inside diameter Standard temperature Flowing velocity at upstream tap Volume Volume at base conditions Flowing volume at upstream tap Ratio of differential pressure to absolute static pressure Ratio of differential pressure to absolute static pressure at the upstream pressure tap Ratio of differential pressure to absolute static pressure at the downstream pressure tap Acoustic ratio Expansion factor Expansion factor based on upstream absolute static pressure Expansion factor based on downstream absolute static pressure Compressibility Compressibility at base conditions Compressibility of air at 14.73 psia and 60F Compressibility of the gas at base conditions

    Compressibility at flowing conditions (6, TI) Compressibility at upstream flowing conditions Compressibility at downstream flowing conditions Compressibility at standard conditions (e9 T,) Linear coefficient of thermal expansion Linear coefficient of thermal expansion of the orifice plate material Linear coefficient of thermal expansion of the meter tube material Ratio of orifice plate bore diameter to meter tube internal diameter (d /D) calculated at flowing temperature, TI Absolute viscosity of flowing fluid

    (Pb8 Tb)

    14.73 ibf/in2 (abs) ft3/hr Ibm/sec Ibm/hr

    ft3/hr 1 545.35 (lbf-ft)/(lb-mol-oR)

    OR "R "R OR OR

    -

    68F 5 l9.67"R ftlsec f e ft3 ft3

    - - - 0.999590

    - idin-"F

    in/in-"F

    iIl/in-"F

    - lbm/ft-sec

  • 4 CHAPTER 1 '&NATURAL GAS FLUIDS MEASUREMENT

    K Universal constant pb Density of a fluid at base conditions (Pb, Tb)

    pb,,ir Density of air at base conditions (Pb, Tb) Pbtm Density of a gas at base conditions (& Tb)

    ps Density of a fluid at standard conditions

    p,@ Density of a fluid at flowing conditions

    pfp, Density of a fluid at flowing conditions at upstream tap position (QI, T f )

    pf,pz Density of a fluid at flowing conditions at downstream tap position (e2, T f )

    (e9 T,)

    (49 T f )

    @i Mole fraction of component Note: Factors, ratios and coefficients are dimensionless.

    3.14159 lbm/ft3 lbm/ft3 Ibm/ft3

    lbm/ft3

    Ibm/ft3

    lbm/f?

    lbm/ft3 %/loo

    3.2.3 TERMINOLOGY

    3.2.3.1 Pressure

    One pound force (lbf) per square inch pressure is defined as the force a 1-pound mass (lbm) exerts when evenly distributed on an area of 1 square inch and when acted on by the standard acceleration of free fall, 32.1740 feet per second per second.

    3.2.3.2 Subscripts

    The subscript 1 on the expansion factor (YJ, the flowing density (pf,pl), the fluid flowing static pressure (P,), and the fluid flowing compressibility (Zh) indicates that these variables are to be measured, calculated, or otherwise determined relative to the fluid flowing at the conditions of the upstream differential tap. Variables related to the downstream differential pressure tap are identified by the subscript 2, including Y,, pf,p2, pf,, and Zf2, and can be used in the equations with equal precision of the calculated flow rates (except for yZ, which has a separate equation).

    The subscript 1 is arbitrarily used in the equations in this part to emphasize the necessity of maintaining the relationship of these four variables to the chosen static pressure reference tap.

    3.2.3.3 Temperature

    The temperature of the flowing fluid (Tf) does not have a numerical subscript. This tem- perature is usually measured downstream of the orifice plate for minimum flow disturbance but may be measured upstream within the locations prescribed in Part 2. It is assumed that there is no difference between fluid temperatures at the two differential pressure tap loca- tions and the measurement point, so the subscript is unnecessary.

    3.2.3.4 Standard Conditions

    Standard conditions are defined as a designated set of base conditions. In this part, stan- dard conditions are defined as the absolute static pressure, P,, of 14.73 pounds force per square inch absolute; the absolute temperature, T,, of 519.67'R (60'F); and the fluid com- pressibility, Z,, for a stated relative density (specific gravity), G.

    3.2.3.5 Definitions

    porated in the text. General definitions are covered in Parts 1 and 2. Definitions specific to Part 3 are incor-

  • A P I MPMS*LY.3 -3 72 = 0732270 0503856 536 ~

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3 - N A T U W GAS APPLICATIONS 5

    3.3 Flow Measurement Equations 3.3.1 GENERAL

    The following equations express flow in terms of mass and volume per unit time and pro- duce equivalent results. Since this section deals exclusively with the inch-pound system of units, the numeric constants defined in Part 1 have been converted to reflect these units.

    The numeric constants for the basic flow equations, unit conversion values, density of water, and density of air are given in 3.5 and Appendix 3-G. The tables in this part that list solutions to these equations incorporate these constants and values. Other physical proper- ties are given in 3.5. Key equation components are developed in 3.4.

    3.3.2 The equations for the mass flow of natural gas, in pounds mass per hour, can be devel-

    oped from the density of the flowing fluid (see Appendix 3-G), the ideal gas relative density (specific gravity), or the real gas relative density (specific gravity), using the following equations.

    The mass flow developed from the density of the flowing fluid (p,J is expressed as fol- lows:

    EQUATIONS FOR MASS FLOW OF NATURAL GAS

    Mass flow developed from the ideal gas relative density (specific gravity), Gi, is ex- pressed as follows:

    The mass flow equation developed from the real gas relative density (specific gravity), G,, assumes a pressure of 14.73 pounds force per square inch absolute and a temperature of 519.67"R (60F) as the reference base conditions for the determination of real gas rela- tive density (specific gravity). This assumption allows the base compressibility of air at 14.73 pounds force per square inch absolute and 519.67"R (60F) to be incorporated into the numeric constant of the flow rate equation. If the assumption about the base reference conditions is not valid, the results obtained from this flow rate equation will have an added increment of uncertainity. The mass flow equation developed from real gas relative density (specific gravity), G,, is expressed as follows:

    Where:

    cd(m) = coefficient of discharge for flange-tapped orifice meter. d = orifice plate bore diameter, in inches, calculated at flowing temperature (Tf).

    E, = velocity of approach factor. Gi = ideal gas relative density (specific gravity). G, = real gas relative density (specific gravity). h, = orifice differential pressure, in inches of water at 60F. Pr, = flowing pressure at upstream tap, in pounds force per square inch absolute. Q, = mass flow rate, in pounds mass per hour.

    Tf = flowing temperature, in degrees Rankine. Y, = expansion factor (upstream tap). 2, = compressibility at standard conditions (e, T,). Z,, = compressibility at upstream flowing conditions (el, Tf).

    pip, = density of the fluid at upstream flowing conditions (el, q, and Z,,), in pounds mass per cubic foot.

  • 6 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    3.3.3 EQUATIONS FOR VOLUME FLOW OF NATURAL GAS The volume flow rate of natural gas, in cubic feet per hour at base conditions, can be de-

    veloped from the densities of the fluid at flowing and base conditions and the ideal gas rel- ative density (specific gravity) or real gas relative density (specific gravity) using the following equations.

    The volume flow rate at base conditions, Q6, developed from the density of the fluid at flowing conditions (P,,~,) and base conditions (pb) is expressed as follows:

    359. 072Cd(FT) EvY,d2 Q6 =

    P b

    (3-4a)

    The volume flow rate at base conditions, developed from ideal gas relative density (specific gravity), Gi, is expressed as follows:

    (3-5a)

    To correctly apply the real gas relative density (specific gravity) to the flow calculation, the reference base conditions for the determination of real gas relative density (specific gravity) and the base conditions for the flow calculation must be the same. Therefore, the volume flow rate at base conditions, developed from real gas relative density (specific gravity), G,., is expressed as follows:

    Qb = 218.573Cd(FI')E,Y,d - fi z;{T (3-6a) If standard conditions are substituted for base conditions in Equations 3-4a, 3-5a, and 3-

    6a, then P b = 4

    = 14.73 pounds force per square inch absolute

    = 519.67"R (60F)

    = 0.999590

    T , = T ,

    z6,,;r = zsoir

    The volume flow rate at standard conditions, Qb, can then be determined using the follow- ing equations.

    The volume flow rate at standard conditions, developed from the density of the fluid at flowing conditions (P,,~,) and standard conditions (p,), is expressed as follows:

    359.072Cd(FT)EvY,d21/P,,h,

    Ps Qv = (3-4b)

    The volume flow rate at standard conditions, developed from ideal gas relative density (specific gravity), Gi, is expressed as follows:

    (3-5b)

    The volume flow rate equation at standard conditions, Q,, developed from the real gas rel- ative density (specific gravity), requires standard conditions as the reference base conditions for G, and incorporates at 14.73 pounds force per. square inch absolute and 519.67"R (60F) in its numeric constant. Therefore, the volume flow rate at standard conditions, de- veloped from real gas relative density ,(specific gravity), G,., is expressed as follows:

    (3-6b) r ; l ~ s h w iG Q, = 7709.61Cd(FI')Ev~d2

  • - - - - _ _ _ _ A P I MPMS*LLI.3.3 ~ 72 0732290 0503858 309

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 7

    Where: C,(FT) = coefficient of discharge for flange-tapped orifice meter.

    d = orifice plate bore diameter calculated at flowing temperature (Tf), in inches. E, = velocity of approach factor. Gi = ideal gas relative density (specific gravity). G, = real gas relative density (specific gravity). h, = orifice differential pressure, in inches of water at 60F. P b = base pressure, in pounds force per square inch absolute. 5, = flowing pressure (upstream tap), in pounds force per square inch absolute. e = standardpressure

    Qb = volume flow rate per hour at base conditions, in cubic feet per hour. Q, = volume flow rate per hour at standard conditions, in cubic feet per hour. Tb = base temperature, in degrees Rankine. T f = flowing temperature, in degrees Rankine. T, = standard temperature

    = 519.67"R (60F). yi = expansion factor (upstream tap). z b = compressibility at base conditions (pbt Tb).

    zbo, = compressibility of air at base conditions (Pb, Tb). Zfl = compressibility at upstream flowing conditions (ei, Tf). 2, = compressibility at standard conditions (e, z).

    Z,, = compressibility of air at standard conditions (e, T,). pb = density of the flowing fluid at base conditions (Pb, Tb), in pounds mass per cu-

    ps = density of the flowing fluid at standard conditions (e, K), in pounds mass per p,pI = density of the fluid at upstream flowing conditions (GI, Tf), in pounds mass per

    = 14.73 pounds force per square inch absolute.

    bic foot.

    cubic foot.

    ciibic foot.

    3.3.4 For the purposes of Part 3, standard and base conditions are assumed to be the same.

    However, if base conditions are different from standard conditions, the volume flow rate calculated at standard conditions can be converted to the volume flow rate at base condi- tions through the following relationship:

    VOLUME CONVERSION FROM STANDARD TO BASE CONDITIONS

    Where: P b = base pressure, in pounds force per square inch absolute. P, = standard pressure, in pounds force per square inch absolute.

    Qb = base volume flow rate, in cubic feet per hour. Q, = standard volume flow rate, in cubic feet per hour. Tb = base temperature, in degrees Rankine. T, = standard temperature, in degrees Rankine. Zb = compressibility at base conditions (Pb, &). 2, = compressibility at standard conditions (E, T,).

    3.4 Flow Equation Components Requiring Additional Computation 3.4.1 GENERAL

    developed in this section. Some of the terms in Equations 3-1 through 3-6 require additional computation and are

  • A P I MPMS*L4*3-3 92 m 0732290 0503859 245 m

    8 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    3.4.2 DIAMETER RATIO (/3) The diameter ratio (), which is used in determining (a) the orifice plate coefficient of dis-

    charge (C,), (b) the velocity of approach factor (E"), and (c) the expansion factor (Y) , is the ratio of the orifice bore diameter (d) to the internal diameter of the meter tube (0). For the most precise results, the actual dimensions should be used, as determined in Parts 1 and 2.

    = d I D (3-8) Where

    d = d,[ l + a,(? - T,)] (3-9) And

    D = D,[l + a,(? - q) ] (3-10) Where:

    d = orifice plate bore diameter calculated at flowing temperature, q. d, = reference orifice plate bore diameter calculated at reference temperature, T,. D = meter tube internal diameter calculated at flowing temperature, q. D, = reference meter tube internal diameter calculated at reference temperature, T..

    T, = reference temperature for the orifice plate bore diameter and/or the meter tube in-

    a, = linear coefficient of thermal expansion of the orifice plate material (see Table 3-1). a, = linear coefficient of thermal expansion of the meter tube material (see Table 3-1).

    = temperature of the fluid at flowing conditions.

    ternal diameter.

    = diameterratio. Note: a, q, and T, must be in consistent units. For the purpose of this standard, T, is assumed to be 68F.

    T, are the diameters determined in accordance with Part 2. The orifice plate bore diameter, d,, and the meter tube internal diameter, Dr, calculated at

    3.4.3 COEFFICIENT OF DISCHARGE FOR FLANGE-TAPPED ORIFICE METER, Cd(FT)

    The coefficient of discharge for a flange-tapped orifice meter (C,) has been determined from test data. It has been correlated as a function of diameter ratio (), tube diameter, and pipe Reynolds number. In this part, the equation for the flange-tapped orifice meter coefficient of discharge developed in Part 1 has been adapted to the inch-pound system of units.

    The equation for the concentric, square-edged flange-tapped orifice meter coefficient of discharge, C,(FT), developed by Reader-Harris and Gallagher, is structured into distinct

    Table 3-1-Linear Coefficient of Thermal Expansion

    Material

    Linear Coefficient of Thermal Expansion (a),

    in/in-OF

    o p e 304 and 316 stainless steel" Monela Carbon steelb

    0.00000925 0.00000795 0.00000620

    Note: For flowing temperature conditions other than those stated in Foot- notes a and b and for other materials, refer to the American Society for Met- als Metals Handbook (Desk Edition, 1985). aFor flowing conditions between -100F and +30O0F, refer to the American Society of Mechanical Engineers data in PTC 19.5, Application, Part II of Fluid Meters: Supplement on Instruments and Apparatus. ?or flowing conditions between-7'F and +154'F, refer to Chapter 12, Sec- tion 2.

  • A P I MPMS*L4-3*3 92 m 0732290 0503Bb0 Tb7 m

    SECTION 3--CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 9

    linkage terms and is considered to best represent the current regression data base. The equa- tion is applicable to nominal pipe sizes of 2 inches and larger; diameter ratios () of 0.1-0.75, provided the orifice plate bore diameter, d,, is greater than 0.45 inches; and pipe Reynolds numbers (ReD) greater than or equal to 4000. For orifice diameters, diameter ra- tios, and pipe Reynolds numbers outside the stated limits, the uncertainty statement in- creases. For guidance, refer to Part 1, 1.12.4.1,

    The Reader-HanisIGallagher equation is defined as follows:

    Cd(FT) = Ci(FT) + 0.000511 (lo:!)"' - + (0.0210 + 0.0049A)4C Ci(FT) = Ci(CT) + Tap Term Ci(CT) = 0.5961 + 0.02912 - 0.22908 + 0.003(1 - ) M ,

    Tap Term = Upstrm + Dnstrm Upstrm = [0.0433 + 0.0712e-8.5L1 - 0.1145e-"oL1](1 - 0.23A)B Dnstrm = -0.0116[M2 - 0.52M2'.3]'.1(1 - 0.14A)

    Also,

    B E - - - - 4 1 - 4

    0.8 19,ooo

    = (Re,)

    (3-11)

    (3-12)

    (3-13)

    (3-14)

    (3-15)

    (3-16)

    (3-17)

    (3-18)

    (3-19)

    (3-20)

    (3-21)

    Where:

    cd(l?) = coefficient of discharge at a specified pipe Reynolds number for a flange-

    Ci(CT) = coefficient of discharge at an infinite pipe Reynolds number for a corner-

    Ci(FT) = coefficient of discharge at an infinite pipe Reynolds number for a flange-

    tapped orifice meter.

    tapped orifice meter.

    tapped orifice meter. d = orifice plate bore diameter calculated at T, in inches.

    D = meter tube internal diameter calculated at T, in inches. e = Napierianconstant

    = 2.71828.

    = dimensionless correction for tap location = N4/D for flange taps.

    N4 = 1 .O when D is in inches.

    L, = L,

    Re, = pipe Reynolds number. = diameterratio

    = d lD. Note: The equation for the coefficient of discharge for a flange-tapped orifice meter, C,(FT), is different from those included in prior editions of this standard.

  • A P I M P M S * 1 4 . 3 . 3 92 0732290 0503863 9T3 m-

    10 CHAPTER I4-NATURAL GAS FLUIDS MEASUREMENT

    3.4.4 VELOCITY OF APPROACH FACTOR (E,)

    The velocity of approach factor (E,) is a mathematical expression that relates the velocity of the flowing fluid in the orifice meter approach section (upstream meter tube) to the fluid velocity in the orifice plate bore.

    The velocity of approach factor, E,, is calculated as follows:

    Where:

    (3-22)

    E, = velocity of approach factor. p = diameterratio

    = d f D .

    3.4.5 REYNOLDS NUMBER (Re,,)

    The pipe Reynolds number (ReD) is used as a correlation parameter to represent the change in the orifice plate coefficient of discharge with reference to the meter tube diameter, the fluid flow rate, the fluid density, and the fluid viscosity. The use of the pipe Reynolds number is an additional change from prior editions of this standard. The Reynolds number is a dimensionless ratio when consistent units are used and is expressed as follows:

    Or

    (3-23)

    (3-24)

    Note: The constant, 12, in the denominator of Equation 3-23 is required by the use of D in inches.

    The fluid velocity can be obtained in terms of the volumetric flow rate at base conditions from the following relationship:

    Substituting Equation 3-25 into Equation 3-23 results in the following relationship:

    (3-25)

    (3-26)

    The Reynolds number for natural gas can be approximated by substituting the following relationship for pb (see 3.5.5.3 for equation development) into Equation 3-26:

    (3-27)

    (3-28)

  • __ A P I MPMS*14.3.3 92 0732290 0503862-83T ~ W

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART Q-NATURAL GAS APPLICATIONS 11

    By using an average value of 0.0000069 pounds mass per foot-second for ,u and substituting the standard conditions of 519.67"R, 14.73 pounds force per square inch, and 0.999590 for &, Pb, and zboir, Equation 3-28 reduces to the following:

    Re, = 47.0723- (3-29) QvGr D

    Where:

    D = meter tube internal diameter calculated at the flowing temperature ( T f ) , in inches. G, = real gas relative density (specific gravity). Pb = base pressure. Qb = volume flow rate at base conditions, in cubic feet per hour. qm = mass flow rate, in pounds mass per second. Q, = volume flow rate at standard conditions, in cubic feet per hour.

    Tb = base temperature, in degrees Rankine. U, = velocity of the flowing fluid at the upstream tap location, in feet per second.

    Re, = pipe Reynolds number.

    = compressibility of air at 14.73 pounds force per square inch absolute and 60F. = compressibility of the gas at base conditions (Pbi Tb).

    ,u = absolute (dynamic) viscosity, in pounds mass per foot-second. ~t = 3.14159.

    P b = density of the flowing fluid at base conditions (pb, Tb), in pounds mass per cubic foot.

    = density of the fluid at upstream flowing conditions (el, T f ) , in pounds mass per cubic foot.

    If the fluid being metered has a viscosity, temperature, or real gas relative density (specific gravity) quite different from those shown above, the assumptions are not applic- able. For variations in viscosity from 0.0000059 to 0.0000079 pounds mass per foot-sec- ond, variations in temperature from 30F to 9OoF, or variations in real gas relative density (specific gravity) from 0.55 to 0.75, the variation should not be significant in terms of its ef- fect on the orifice plate coefficient of discharge at higher Reynolds numbers.

    When the flow rate is not known, the Reynolds number can be developed through itera- tion, assuming an initial value of 0.60 for the coefficient of discharge for a flange-tapped orifice meter, C,(FT), and using the volume computed to estimate the Reynolds number.

    3.4.6 EXPANSION FACTOR (Y) 3.4.6.1 General

    When a gas flows through an orifice, the change in fluid velocity and static pressure is ac- companied by a change in the density, and a factor must be applied to the coefficient to ad- just for this change. The factor is known as the expansion factor ( Y ) and can be calculated from the following equations taken from the report to the A.G.A. Committee by the Na- tional Bureau of Standards datedMay 26,1934, and prepared by Howard S . Bean. The ex- pansion factor ( Y ) is a function of diameter ratio @), the ratio of differential pressure to static pressure at the designated tap, and the isentropic exponent (k).

    The real compressible fluid isentropic exponent, k,, is a function of the fluid and the pres- sure and temperature. For an ideal gas, the isentropic exponent, ki, is equal to the ratio of the specific heats (c,/cv) of the gas at constant pressure (c,) and constant volume (c,,) and is independent of pressure. A perfect gas is an ideal gas that has constant specific heats. The perfect gas isentropic exponent, k,, is equal to ki evaluated at base conditions.

    It has been found that for many applications, the value of k, is nearly identical to the value of ki, which is nearly identical to kp. From a practical standpoint, the flow equation is

  • A P I MPMS*L4*3-3 92 0732290 0503863 776 =

    12 CHAPTER 1 &-NATURAL GAS FLUIDS MEASUREMENT

    not particularly sensitive to small variations in the isentropic exponent. Therefore, the per- fect gas isentropic exponent, kp, is often used in the flow equation. Accepted practice for natural gas applications is to use k, = k = 1.3. This greatly simplifies the calculations and is used in the tables. This approach was adopted by Buckingham in his correlation for the expansion factor.

    The application of the expansion factor is valid as long as the following dimensionless criterion for pressure ratio is followed:

    O < I 0.20 hW 27.707 4

    Or

    P 0.8 I < 1.0

    G

    (3-30)

    (3-31)

    Where:

    h, = flange tap differential pressure across the orifice plate, in inches of water at 60F. pf = flowing pressure, in pounds force per square inch absolute.

    p f l = absolute static pressure at the upstream pressure tap, in pounds force per square

    P, = absolute static pressure at the downstream pressure tap, in pounds force per square

    The expansion factor equation for flange taps may be used for a range of diameter ratios from 0.10 to 0.75. For diameter ratios () outside the stated limits, increased uncertainty will occur.

    inch absolute.

    inch absolute.

    3.4.6.2 Expansion Factor Referenced to Upstream Pressure

    of the expansion factor, Y,, can be calculated using the following equation: If the absolute static pressure is taken at the upstream differential pressure tap, the value

    = 1 - (0.41 + 0.354) i (3-32) When the upstream static pressure is measured,

    X I = G - 4 2 = hw G 27.707 4,

    When the downstream static pressure is measured,

    - hW X I = G - I;, - G2 + (G - G2) 27.707G2 + h,

    Where:

    (3-33)

    (3-34)

    h, = differential pressure, in inches of water at 60F.

    Pr, = absolute static pressure at the upstream tap, in pounds force per square inch ab-

    e2 = absolute static pressure at the downstream tap, in pounds force per square inch ab- x, = ratio of differential pressure to absolute static pressure at the upstream tap. Y, = expansion factor based on the absolute static pressure measured at the upstream

    = diameter ratio (d/D).

    k = isentropic exponent (see 3.4.6.1).

    solute.

    solute.

    tap.

    The quantity x , / k is known as the acoustic ratio.

  • SECTDN 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 13

    3.4.6.3 Expansion Factor Referenced to Downstream Pressure

    expansion factor, yZ, can be calculated using the following equation: If the absolute static pressure is taken at the downstream differential tap, the value of the

    And

    Or

    And

    x, = G - % = h w $2 27.707 Gl

    (3-35)

    (3-36)

    (3-37)

    (3-38)

    Where: h, = differential pressure, in inches of water at 60F.

    4, = absolute static pressure at the upstream tap, in pounds force per square inch ab-

    Pr, = absolute static pressure at the downstream tap, in pounds force per square inch ab-

    x, = ratio of differential pressure to absolute static pressure at the upstream tap. x2 = ratio of differential pressure to absolute static pressure at the downstream tap. yi = expansion factor based on the absolute static pressure measured at the upstream tap. y2 = expansion factor based on the absolute static pressure measured at the downstream

    Zh = Compressibility at upstream flowing conditions (e,, T f ) . Z,, = compressibility at downstream flowing conditions ( p f , , q).

    k = isentropic exponent (see 3.4.5.1).

    solute.

    solute.

    tap.

    = diameter ratio (d/D). Note: xz equals the ratio of the differentid pressure to the static pressure at the downstream tap (p/,, .

    3.5 Gas Properties 3.5.1 GENERAL

    The measurement of gaseous flow rate in volume units under other than standard or base conditions requires conversion for pressure, temperature, and the deviation of the measured volume from the ideal gas laws (compressibility). Energy measurement also requires adjust- ment for heat content. The standard conditions used in Part 3 are a base pressure of 14.73 pounds force per square inch absolute and a base temperature of 5 19.67"R (60F).

    As a mixture of compounds, natural gas complicates the calculation of some of these conversion factors. The factors that cannot be determined by simple calculations can be de- rived from gas composition and/or other measurements. Certain factors can be measured in the field, using instruments calibrated against standard gas samples. Either approach will produce equivalent results when rigorous methods are applied.

    3.5.2 PHYSICAL PROPERTIES Table 3-F-1 in Appendix 3-F lists physical properties taken from GPA 2145-91. The data

    for ideal density and ideal heating value per cubic foot from GPA 2145-91 have, where nec-

  • 14 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    essary, been corrected in Table 3-F-1 for the base pressure of 14.73 pounds force per square inch absolute through the following relationship:

    Table 3-F-lvalue = - 14*73 x GPA 2145-91 table value (3-39) 14.696

    Table 3-F-1 provides the best currently available data on physical properties. These data are subject to modification yearly as additional research is accomplished. Future revisions to GPA 2145 may include updated values. The values from the most recent edition of GPA 2145 should be used, and the values for density and British thermal units per cubic foot should be corrected through the use of Equation 3-39.

    In addition, GPA Publication 2172 and Publication 18 1 are incorporated in this standard as the method of calculating heating values of natural gas mixtures from compositional analysis. An abbreviated form of that methodology is included in Appendix 3-F as a refer- ence.

    In this edition, the compressibility of air at standard conditions (Zsoir) has been updated to the value of 0.999590.

    3.5.3 COMPRESSIBILITY

    3.5.3.1 Ideal and Real Gas

    The terms ideal gas and real gas are used to dene calculation or interpretation methods. An ideal gas is one that conforms to the thermodynamic laws of Boyle and Charles (ideal gas laws), such that the following is true:

    144PV = nRT (3-40)

    If Subscript 1 represents a gas volume measured at one set of temperature-pressure con- ditions and Subscript 2 represents the same volume measured at a second set of tempera- ture-pressure conditions, then

    (3-41)

    The numerical constant in Equation 3-40 is required to convert P, in pounds force per square inch absolute, to units that are consistent with the value of R given in Part 2.

    All gases deviate from the ideal gas laws to some extent. This deviation is known as compressibility and is denoted by the symbol Z . Additional discussion of compressibility and the method for determining the value of 2 for natural gas are developed in detail in A.G.A. Transmission Measurement Committee Report No. 8. The method used in that re- port is included as a part of this standard.

    The application of Z changes the ideal relationship in Equation 3-40 to the following real relationship:

    4% = eV, I; T,

    144PV = nZRT (3-42)

    As modified by Z , Equation 3-41 allows the volume at the upstream flowing conditions to be converted to the volume at base conditions by use of the following equation:

    (3-43)

    Where:

    ri = number of pound-moles of a gas. P = absolute static pressure of a gas, in pounds force per square inch absolute. Pb = absolute static pressure of a gas at base conditions, in pounds force per square inch

    absolute.

  • SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 15

    el = absolute static pressure of a gas at the upstream tap, in pounds force per square R = universal gas constant

    T = absolute temperature of a gas, in degrees Rankine. Tb = absolute temperature of a gas at base conditions, in degrees Rankine. $ = absolute temperature of a flowing gas, in degrees Rankine. V = volume of a gas, in cubic feet. V, = volume of a gas at base conditions (pb, &)i in cubic feet. 5, = volume of a gas at flowing conditions (e,, Tf), in cubic feet. Z = compressibility of a gas at P and T.

    z b = compressibility of a gas at base conditions (& Ti). Zfl = compressibility of a gas at flowing conditions (el, Tf).

    inch absolute.

    = 1545.35 (lbf-ft)/(lbmol-OR).

    3.5.3.2 Compressibility at Base Conditions

    in A.G.A. Transmission Measurement Committee Report No. 8. The value of Z at base conditions ( z b ) is required and is calculated from the procedures

    3.5.3.3 Supercompressibility

    In orifice measurement, z b and 2, appear as a ratio to the 0.5 power. This relationship is termed the sicpercompressibility factor and may be calculated from the following equation:

    Or

    Where:

    (3-44)

    (3-45)

    F,, = supercompressibility Luctor. z b = compressibility of the gas at base conditions (Pb, Tb). Z,, = compressibility of the gas at flowing conditions (el, Tf).

    3.5.4 RELATIVE DENSITY (SPECIFIC GRAVITY)

    3.5.4.1 General

    Relative density (specific gravity), G, is a component in several of the flow equations. The relative density (specific gravity) is defined as a dimensionless number that expresses the ratio of the density of the flowing fluid to the density of a reference gas at the same ref- erence conditions of temperature and pressure. The gas industry has historically referred to the relative density (specific gravity) as either ideal or real and has designated the reference gas as air and the standard reference conditions as a pressure of 14.73 pounds force per square inch absolute and a temperature of 519.67"R (60F). The value for relative density (specific gravity) may be determined by measurement or by calculation from the gas com- position.

    3.5.4.2 Ideal Gas Relative Density (Specific Gravity)

    The ideal gas relative density (specific gravity), Gi, is defined as the ratio of the ideal den- sity of the gas to the ideal density of dry air at the same reference conditions of pressure and temperature. Since the ideal densities are defined at the same reference conditions of pres- sure and temperature, the ratio reduces to a ratio of molar masses (molecular weights).

  • A P I MPMS*L4.3.3 92 I 0732290 0503867 311

    16 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    Therefore, the ideal gas relative density (specific gravity) is set forth in the following equa- tion:

    (3-46)

    Where:

    Gi = ideal gas relative density (specific gravity).

    = 28.9625 pounds mass per pound-mole. Mrair = molar mass (molecular weight) of air

    Mr,,, = molar mass (molecular weight) of a flowing gas, in pounds mass per pound- mole.

    3.5.4.3 Real Gas Relative Density (Real Specific Gravity)

    Real gas relative density (specific gravity), Gr, is defined as the ratio of the real density of the gas to the real density of dry air at the same reference conditions of pressure and tem- perature. To correctly apply the real gas relative density (specific gravity) to the flow cal- culation, the reference conditions for the determination of the real gas relative density (specific gravity) must be the same as the base conditions for the flow calculation. At ref- erence (base) conditions (P', Tb), real gas relative density (specific gravity) is expressed as fol10 ws :

    G, =

    Since the pressures and temperatures are defined to be at the same designated base con- ditions,

    Pbgar = pboir

    And the real gas relative density (specific gravity) is expressed as follows:

    (3-47)

    The use of real gas relative density (specific gravity) in the flow calculations has a his- toric basis but may add an increment of uncertainty to the calculation as a result of the lim- itations of field gravitometer devices. When real gas relative densities (specific gravities) are directly determined by relative density measurement equipment, the observed values must be adjusted so that both air and gas measurements reflect the same pressure and tem- perature. The fact that the temperature and/or pressure are not always at base conditions re- sults in small variations in determinations of relative density (specific gravity). Another source of variation is the use of atmospheric air. The composition of atmospheric air-and its molecular weight and density-varies with time and geographical location.

    When recording gravitometers are used and calibration is performed with reference gases, either ideal or real gas relative density (specific gravity) can be obtained as a recorded relative density (specific gravity) by proper certification of the reference gas. The relationship between ideal gas relative density (specific gravity) and real gas relative den- sity (specific gravity) is expressed as follows:

    Gr = Gi - Zhou (3-48) ' b g m

  • A P I M P M S * l 4 - 3 - 3 92 0732290 0503868 258 W

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 17

    W

    = &biMC

    Where: Gi = ideal gas relative density (specific gravity). Gr = real gas relative density (specific gravity).

    = 28.9625 pounds mass per pound-mole. Mr,, = molar mass (molecular weight) of air

    Mrgos = molar mass (molecular weight) of the flowing gas, in pounds mass per pound-

    Pb = absolute static pressure of a gas at base conditions, in pounds force per square mole.

    inch absolute. = base pressure of air, in pounds force per square inch absolute.

    Pbgor = base pressure of a gas, in pounds force per square inch absolute. R = universal gas constant

    & = absolute temperature of a gas at base conditions, in degrees Rankine. = 1545.35 (Ibf-ft)/(lbmol-OR).

    Tbdi, = base temperature of air, in degrees Rankine. Tbga, = base temperature of a gas, in degrees Rankine.

    = compressibility of air at base conditions (Pbi Tb). = compressibility of a gas at base conditions (Pi,, Tb).

    3.5.5

    3.5.5.1 General

    The flowing density (p,,) is a key component of certain flow equations. It is defined as the mass per unit volume at flowing pressure and temperature and is measured at the se- lected static pressure tap location. The value for flowing density can be calculated from equations of state or from the relative density (specific gravity) at the selected static pres- sure tap. The fluid density at flowing conditions can also be measured using commercial densitometers. Most densitometers, because of their physical installation requirements and design, cannot accurately measure the density at the selected pressure tap location. There- fore, the fluid density difference between the density measured and that existing at the defined pressure tap location must be checked to determine whether changes in pressure or temperature have an impact on the flow measurement uncertainty.

    An approximation for field calculation is the direct application of tables from the equa- tion of state. Such density tables have considerable bulk if they cover a wide range of con- ditions in small increments. Tables have a further deficiency in that they do not readily lend themselves to interpolation or extrapolation with fluctuating temperature and/or pressure.

    At the time of publication, it was anticipated that a computer program for IBM and com- patible personal computers that generates density and/or compressibility tables for user- defined gas and pressure-temperature ranges would be available through A.G.A. This program uses the equations in A.G.A. Transmission Measurement Committee Report N0.8.

    DENSITY OF FLUID AT FLOWING CONDITIONS

    3.5.5.2 Density Based on Gas Composition

    When the composition of a gas mixture is known, the gas densities p,, and pb may be cal- culated from the gas law equations. The molecular weight of the gas may be determined from composition data, using mole fractions of the components and their respective mole- cular weights.

    M ~ ~ ( L F = $,Mq + $2Mr2 + ... + $&rW (3-49)

    i=l

    In the following, the gas law equation, Equation 3-42, is rearranged to obtain density val- ues:

  • A P I M P M S * L 4 - 3 . 3 92 = 0732290 0503869 194

    18 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    Therefore:

    And

    Or

    144PV = nZRT

    144PV = ( g ] Z R T (3-51)

    (3-52)

    (3-53)

    Where: Gi = ideal gas relative density (specific gravity). m = mass of a fluid, in pounds mass.

    Mroir = molar mass (molecular weight) of air

    Mrgns = molar mass (molecular weight) of the flowing gas, in pounds mass per pound-

    Mr, = molar mass (molecular weight) of a component, in pounds mass per pound-

    = 28.9625 pounds mass per pound-mole.

    mole.

    mole. n = numberof moles. P = absolute static pressure of a gas, in pounds force per square inch absolute. Pb = absolute static pressure of a gas at base conditions, in pounds force per square

    GI = absolute static pressure of a gas at the upstream tap, in pounds force per square

    R = universal gas constant

    T = absolute temperature of a gas, in degrees Rankine. Tb = absolute temperature of a gas at base conditions, in degrees Rankine. Tf = absolute temperature of a flowing gas, in degrees Rankine. V = volume of a gas, in cubic feet. Z = Compressibility of a gas at 8 T.

    z b = compressibility of a gas at base conditions (Pb, Tb). Z,, = compressibility of a gas at flowing conditions (el, Tf). p b = density of a gas at base conditions (Pb, &), in pounds mass per cubic foot.

    inch absolute.

    inch absolute.

    = 1545.35 (lbf-ft)/(lbmol-OR).

    ptPi = density of a gas at upstream flowing conditions (e,, Tf), in pounds mass per cu- bic foot.

    @i = mole fraction of a component.

    3.5.5.3 Density Based on Ideal Gas Relative Density (Specific Gravity) The gas densities P,,~, and p b may be calculated from the ideal gas relative density

    (specific gravity), as defined in 3.5.5.2. The following equations are applicable when a gas analysis is available:

    (3-46)

  • A P I M P M S * 1 4 . 3 - 3 92 W 0732290 0503870 706 -~

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 19

    Note: Themolecular weight of dry air, from GPA 2145-91, is given as 28.9625 pounds mass per pound-mole (ex- actly).

    MG^^ = G.Mcir = G.(28.9625) (3-54) Substituting for Mrgos in Equations 3-52 and 3-53, p,pi and pb are determined as follows:

    $GI: (28.9625)(144) - ZART

    P,,P, -

    And

    eG.(28.9625)(144)

    ' b R T P b =

    eci = 2.69881- ' b Tb

    Where:

    (3-55)

    (3-56)

    Gi = ideal gas relative density (specific gravity).

    = 28.9625 pounds mass per pound-mole. Mr,, = molar mass (molecular weight) of air

    Mrnos = molar mass (molecular weight) of a flowing gas, in pounds mass per pound-

    Pb = absolute static pressure of the gas at base conditions, in pounds force per square

    el = absolute static pressure of a gas at the upstream tap, in pounds force per square R = universal gas constant

    5 = absolute temperature of a gas at base conditions, in degrees Rankine. T f = absolute temperature of a flowing gas, in degrees Rankine.

    z b = compressibility of a gas at base conditions (pb, Tb). Zfl = compressibility of a gas at flowing conditions (e,, T f ) . pb = density of a gas at base conditions (Pbi Tb, and zb), in pounds mass per cubic

    plei = density of a gas at upstream flowing conditions (el, j, and ZfJ, in pounds mass

    mole.

    inch absolute.

    inch absolute.

    = 1545.35 (lbf-ft)/(lbmol-oR).

    foot.

    per cubic foot.

    3.5.5.4 Density Based on Real Gas Relative Density (Specific Gravity)

    (specific gravity) is given by the following equation: The relationship of real gas relative density (specific gravity) to ideal gas relative density

    G, = Gi - zb,, (3-48) -%

    Or

    G. = G, -% zh,,

    Note: The real gas relative density (specific gravity) of dry air at base conditions is defined as exactly 1.00000.

    Substituting for Gi in Equations 3-55 and 3-56 results in the following:

  • API MPMS*14.3.3 92 W 0732290 0 5 0 3 8 7 1 842 W

    20 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    2.6988 14 G,. n. = P b Tb 'b,,

    (3-57)

    (3-58)

    To correctly apply the density equations, Equations 3-57 and 3-58, which were devel- oped from the real gas relative density (specific gravity), to the flow calculation, the refer- ence base conditions for the determination of real gas relative density (specific gravity) and the base conditions for the flow calculation must be the same. When standard conditions are substituted for base conditions,

    P b = = 14.73 pounds force per square inch absolute

    = 519.67"R (60'F)

    = 0.999590

    Tb = T,

    -Goir = z,,

    The gas density based on real gas relative density (specific gravity) is given by the follow- ing equations:

    - 2 . 6 9 a a i 5 ~ , z , ~ ~ O. 999590 Zh A,,, -

    And

    (2.69881)(14.73)Gr (O. 999590)(5 19.67) ps =

    = O. 0765289 G,

    (3-59)

    (3-60)

    Where: Gi = ideal gas relative density. G, = real gas relative density. Pb = absolute static pressure of a gas at base conditions, in pounds force per square

    4, = absolute static pressure of a gas at the upstream tap, in pounds force per square

    T6 = absolute temperature of a gas at base conditions, in degrees Rankine. Tf = absolute temperature of a flowing gas, in degrees Rankine.

    inch absolute.

    inch absolute.

    ZbOir = compressibility of air at base conditions (Pb, Tb). = compressibility of a gas at base conditions (Pb, Tb).

    Z, = compressibility of a gas at flowing conditions (e,, Tf). Z,, = compressibility of air at standard conditions (4, T,). Zsgns = compressibility of a gas at standard conditions (4, T,).

    p b = density of a gas at base conditions (Pb, Tb, and zb), in pounds mass per cubic foot. ps = density of a gas at standard conditions (4, T,, and Z,), in pounds mass per cubic foot.

    p,,,, = density of a gas at upstream flowing conditions (e,, Tf, and Zf,), in pounds mass The density equations for standard conditions based on the real gas relative density (specific gravity) developed above require standard conditions as the designated reference base con- ditions for G, and incorporate &,,, at 14.73 pounds force per square inch absolute and 519.67"R in their numeric constants.

    per cubic foot.

  • APPENDIX 3-A-ADJUSTMENTS FOR INSTRUMENT CALIBRATION

    3-A.l Scope This appendix provides equations and procedures for adjusting and correcting field mea-

    surement calibrations of secondary instruments.

    3-A.2 General Field practices for secondary instrument calibrations and calibration standard applica-

    tions contribute to the overall uncertainty of flow measurement. Calibration standards for differential pressure and static pressure instruments are often

    used in the field without local gravitational force adjustment or correction of the values in- dicated by the calibrating standards. For example, it is common to use water column manometers to calibrate differential pressure instruments without making field corrections to the manometer readings for changes in water density. The manometer readings are af- fected by local gravitational effects, water temperatures, and the use of other than distilled water.

    Pressure devices that employ weights are also used to calibrate differential pressure in- struments without correction for the local gravitational force. Similarly, deadweight testers are used to calibrate static pressure measuring equipment without correction for the local gravitational force. It is usually more convenient and accurate to incorporate these adjust- ments in the flow computation than for the person calibrating the instrument to apply these small corrections during the calibration process. Therefore, additional factors are added to the flow equation for the purpose of including the appropriate calibration standard correc- tions in the flow computation either by the flow calculation procedure in the office or by the meter technician in the field.

    Six factors are provided that may be used individually or in combination, depending on the calibration device and the calibration procedure used:

    Correction for air over the water in the water manometer during the differential in- strument calibration. Local gravitational correction for the water column calibration standard. Water density correction (temperature or composition) for the water column calibra- tion standard. Local gravitational correction for the deadweight tester static pressure standard. Manometer factor (correction for the gas column in mercury manometers). Mercury manometer temperature factor (span correction for instrument temperature change after calibration).

    F,,

    FW, FtiI

    FhRni FhRI

    These factors expand the base volume flow equation to the following:

    Q, = Qv e m 4.t 4.t

  • 22

    A P I MPMS*L4.3-3 92 = O732290 0503873 bL5

    CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    applicable; however, if SI units are used, the more generic equations in Part 1 should be used for consistent results.

    3-A.3.2 SYMBOLS AND UNITS Description

    Temperature, in degrees Fahrenheit Temperature, in degrees Rankine Correction for air over the water in the water manometer Manometer factor Mercury manometer temperature factor Local gravitational correction for deadweight tester Local gravitational correction for water column Water density correction Local acceleration due to gravity Acceleration of gravity used to calibrate weights or deadweight calibrator Ideal gas relative density (specific gravity) Real gas relative density (specific gravity) Differential pressure above atmospheric Elevation above sea level Latitude on earth's surface Molar mass of gas Molar mass of air Absolute gas pressure Local atmospheric pressure Base pressure Absolute pressure of flowing gas Volume flow rate at standard conditions modified for instrument calibration adj us tments Universal gas constant Absolute gas temperature Base temperature Absolute temperature of a flowing gas Mercury ambient temperature Gas ambient temperature Compressibility of a gas at T and P Compressibility of a gas at standard conditions (Gr, PbJ and Tb) Compressibility of air at 5 19.67"R Compressibility of air at P,,, and 519.67"R Compressibility of air at 14.73 psia and 519.67"R Compressibility of gas at flowing conditions (Gr, 4, and Tf ) Density of air at pressure above atmospheric Density of atmospheric air Density of gas or vapor in the differential pressure instrument Density of mercury in the differential pressure instrument

    + h, and

    Units/Value - -

    ft/sec2 - -

    inches of water column at 60F ft degrees lbm/ib-mol 28.9625 lbm/ib-mol lbf/inz (abs) lbf/in2 (abs) lbf/in2 (abs) lbf/in2 (abs)

    ft3/hr 1545.35 (Ibf-ft)/(lb-mol-OR) OR OR

    OR O R

    OR -

    0.999590

    -

    lbm/ft3 lbm/ft3

    1bm/ft3

    lbm/ft3

  • A P I MPMS*L4.3.3 92 M 0732290 0503874 5 5 1 M

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 23

    phgc

    phgo

    Density of mercury in the differential pressure instrument at the time of its calibration Density of mercury in the differential pressure instrument at the mercury gauge operating conditions lbm/ft3 Density of water in the manometer at other than 60F lbm/ft3

    lbm/ft3

    pw

    3-A.4 Water Manometer Gas Leg Correction Factor (Ern) The factor F,, corrects for the gas leg over water when a water manometer is used to cal-

    ibrate a differential pressure instrument:

    4 = dpwi. pa (3-A-2) When atmospheric air is used as the medium to pressure both the differential pressure in- strument and the water U-tube manometer during calibration, the density of air at atmos- pheric pressure and 60F must be calculated using the following equation:

    Mr c;. P p = - RZT

    (3-A-3)

    Substituting local atmospheric pressure (e,) for absolute pressure (P), 519.67"R (60F) for the absolute temperature (T), 28.9625 for Mra,, 1.0 for the ideal relative density (specific gravity) of air (GJ, and 1545.35 for the universal gas constant (R) provides the following relationship:

    (28.9625)(1. O)em

    1545*35 Z (519.67) 144 a-

    Pottn =

    (3-A-4)

    The local atmospheric pressure may be calculated using an equation published in the Smith- sonian Meteorological Tables:

    1 55096 - (Elevation, ft - 361) 55096 + (Elevation, ft - 361) t,,,, = 14.54 (3-A-5) The density of air at any given differential pressure (h,) above atmospheric pressure can then be represented by the following:

    (3-A-6)

    The density of water can be obtained from Table 3-A-1 or calculated from the following Wegenbreth density equation:

    p, = 0.0624280[999.8395639 + 0.06798299989q. - 0.009106025564~2 + 0.0001005272999T~ - 0.000001 126713526Tw + 0 . ~ 6 5 9 1 7 9 5 6 0 6 T ~ I

    Where:

    (3-A-7)

    Gi = ideal gas relative density (specific gravity). h, = differential pressure above atmospheric, in inches of water at 60F. Mr = molar mass of a gas, in pounds mass per pound-mole.

  • A P I MPMS*14-3.3 92 W 0732290 0503875 498 W

    24 CHAPTER 1 &-NATURAL GAS FLUIDS MEASUREMENT

    Table 3-A-i-Water Density Based on Wegenbreth Equation

    Temperature Density ("F) (ibm/ft3)

    45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

    62.42 12 62.4193 62.4172 62.4148 62.4 12 1 62.4092 62.4060 62.4026 62.3980 62.3949 62.3908 62.3863 62.3817 62.3768 62.3711 62.3663 62.3608 62.3550

    Temperature Density (OF) (ibm/ft3)

    63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

    62.3490 62.3427 62.3363 62.3297 62.3228 62.3157 62.3085 62.3010 62.2934 62.2855 62.2775 62.2692 62.2608 62.2522 62.2434 62.2344 62.2252 62.2159

    P = absolute gas pressure, in pounds force per square inch absolute.

    R = universal gas constant

    T = absolute gas temperature, in degrees Rankine. T, = temperature of water, in degrees Celsius. 2 = compressibility of a gas at P and T. 2, = compressibility of air at

    p = density of a gas, in pounds mass per cubic foot. pa = density of air at pressure above atmospheric, in pounds mass per cubic foot.

    pIY = density of water in a manometer at a temperature other than 6OoF, in pounds

    etnt = local atmospheric pressure, in pounds force per square inch absolute. = 1545.35 (lbf-ft)/(lbmol-OR).

    + h,, and 519.67"R. = compressibility of air at e,ff1 and 519.67"R.

    palm, = density of atmospheric air, in pounds mass per cubic foot.

    mass per cubic foot.

    3-A.5 Water Manometer Temperature Correction Factor (FJ The factor F,, corrects for variations in the density of water used in the manometer when

    the water is at a temperature other than 60F. The F,, correction factor should be included in the flow measurement computation when a differential instrument is calibrated with a water manometer.

    P," = 62.3663 (3-A-8)

    Where:

    pw = density of water in a manometer at a temperature other than 60"F, in pounds mass per cubic foot.

    3-A.6 Local Gravitational Correction Factor for Water Manometers (Fw,)

    The factor fiv, corrects the weight of the manometer fluid for the local gravitational force. The effect on the quantity is the square root of the ratio of the local gravitational force to

  • A P I M P M S * L 4 - 3 - 3 7 2 U O732270 0503876 324 W ~~

    SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 25

    the standard gravitational force used in the equation derivations. This relationship is ex- pressed as follows:

    (3-A-9)

    Where:

    g, = local acceleration due to gravity, in feet per second per second.

    The local value of gravity at any location may be obtained from a U.S. Coast and Geo- detic Survey reference to aeronautical data or from the Smithsonian Meteorological Tables. Using Equation E l l from the 1985 edition of ANSUAPI 2530 and the 45"-latitude-at-sea- level reference value, approximate values of g, may be obtained from the following curve- fit equation covering latitudes from O" to 90":

    gl = 0.0328095[978.01855 - 0.0028247L + 0.0020299L2 - 0.00001505SL3 - 0.000094HI (3-A- 10)

    Where:

    L = latitude, in degrees. H = elevation, in feet above sea level.

    3-A.7 Local Gravitational Correction Factor for Deadweight Calibrators Used to Calibrate Differential and Static Pressure Instruments (bW,)

    The factor $KI is used to correct for the effect of local gravity on the weights of a dead- weight calibrator. The calibrator weights are usually sized for use at a standard gravitational force or at some specified gravitational force. A correction factor must then be applied to correct the calibrations to the local gravitational force:

    (3-A- 1 1)

    Where:

    g, = acceleration due to local gravitational force, in feet per second per second. go = acceleration of gravity used to calibrate the weights of a deadweight calibrator, in

    When a deadweight calibrator is used for the differential pressure and the static pressure, both must be corrected for local gravity. This involves using

    feet per second per second.

    twice.

    3-A.8 Correction for Gas Column in Mercury Manometer Instruments (hgm)

    The factor FhRm corrects for the gas or vapor leg of fluid at static pressure and the temper- ature of the manometer or other instrument. Mercury U-tube manometers and mercury- manometer-type differential pressure instruments are sometimes used to measure h,. The manometer factor Fhgm is added to the flow equation to correct for the effect of the gas col- umn above the mercury during flow measurements:

    (3-A-12)

    Where:

    phg = density of mercury in the differential pressure instrument, in pounds mass per cu- bic foot. The effect of atmospheric air (usually defined as the weight in vacuo of

  • API MPMS*14.3m3 92 0732290 0503877 260

    26 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

    the mercury sample at the base pressure and temperature defined for the flow mea- surement) is excluded.

    pg = density of the gas or vapor in the differential pressure instrument, in pounds mass per cubic foot. The effect of atmospheric air (usually defined as weight in vacuo of the fluid sample at the flowing pressure existing at the orifice meter during the flow measurement and at the temperature existing at the differential pressure in- strument during the flow measurement) is excluded.

    The density of mercury at ambient temperature Zjga, in degrees Rankine, may be calcu- lated from the following equation:

    phg = 846.324C1.0 - O.OOOlOl(l;,, - 519.67)] (3-A-13)

    The density of a gas at ambient temperature may be calculated using the following equa- tion:

    ' b Gr 5 'bOirR ' f T a s .

    Pg =

    For standard conditions of

    = 14.73 lbf /in2 (abs) q = r

    = 519.67"R (60F)

    = 0.999590

    Then

    (3-A-14)

    (3-A- 15)

    Where:

    G, = real gas relative density (specific gravity).

    = 28.9625 pounds mass per pound-mole. Mrai, = molar mass of air

    6 = absolute pressure of a flowing gas, in pounds force per square inch absolute. R = univeral gas constant

    T, = absolute temperature of a flowing gas, in degrees Rankine. = 1545.3 5 (lbf-ft)/(lbmol-OR) .

    Tgaso = gas ambient temperature, in degrees Rankine. = mercury ambient temperature, in degrees Rankine.

    zb = compressibility of a gas at G,, Tb, and Pb. Zbajr = compressibility of air at 519.67"R and 14.73 pounds force per square inch ab-

    solute = 0.999590.

    Zf = compressibility of a gas at flowing conditions (G,., T,, and e). Zs = compressibility of a gas at 519.67"R and 14.73 pounds force per square inch ab-

    solute.

    Tabular data for &,m are given in Table 3-A-2. Correction for a liquid leg over the mercury can also be made if the liquid density is sub-

    stituted for pg in Equation 3-A-12. If the mercury differential pressure instrument is cali- brated using a water column or a weight calibrator, the Fw,, and F,, factors are also needed.

  • ~-

    A P I M P M S * l Y . 3 . 3 92 H 0732290 0503878 l T 7

    SECTION CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL GAS APPLICATIONS 27

    Table 3-AP-Mercury Manometer Factors (ihg,) ~ ~~

    Real Gas Ambient Relative Temperature Density (OW O 500 loo0 1500 2000 2500 3000

    Static Pressure (pounds force per square inch gauge)

    0.550 O 0.600 O 0.650 O 0.700 O 0.750 O 0.550 20 0.600 20 0.650 20 0.700 20 0.750 20 0.550 40 0.600 40 0.650 40 0.700 40 0.750 40 0.550 60 0.600 60 0.650 60 0.700 60 0.750 60 0.550 80 0.600 80 0.650 80 0.700 80 0.750 80 0.550 100 0.600 100 0.650 100 0.700 100 0.750 100 0.550 120 0.600 120 0.650 120 0.700 120 0.750 120

    1.0030 1.0030 1.0030 1.0030 1.0030 1.0020 1 .o020 1 .o020 1 .o020 1.0020 1.0010 1.0010 1.0010 1.0010 1.0010 1 .oooo 1 .m 1.Oooo 1 .oooo 1 .oooo 0.9990 0.9990 0.9990 0.9990 0.9990 0.9980 0.9980 0.9980 0.9980 0.9980 0.9970 0.9970 0.9970 0.9970 0.9970

    1.0019 1.0018 1.0017 1.0015 1.0014 1.0010 1.0009 1 .O008 1 .O007 1.0005 1 .oooo 0.9999 0.9998 0.9997 0.9996 0.9991 0.9990 0.9989 0.9988 0.9987 0.9981 0.9980 0.9979 0.9978 0.9977 0.9972 0.9971 0.9970 0.9969 0.9968 0.9962 0.9961 0.9960 0.9959 0.9958

    1 .o006 1.0002 0.9997 0.9991 0.9984 0.9997 0.9994 0.9990 0.9985 0.9980 0.9989 0.9986 0.9983 0.9980 0.9975 0.9980 0.9978 0.9975 0.9972 0.9968 0.9971 0.9969 0.9967 0.9964 0.9961 0.9962 0.9960 0.9958 0.